Will computers make mathematicians obsolete?

1. Nov 7, 2012

Mr.Watson

I mean if we someday has quantum computers etc. wouldn't it be able to solve all math problems just by heave number crunching and doing so, wouldn't that meant that every mathematician would be out of job? So is math really bad career for future?

2. Nov 7, 2012

rudolfstr

not really, it you can't crunch most of problems in math just by checking a finite amount of solutions. Most problems have infinite ammount of posible solutions, so checking them all is imposible.

3. Nov 7, 2012

Mentallic

Quantum computers will supposedly only be able to do whatever our current computers can do, just faster.

4. Nov 7, 2012

micromass

Most mathematics problems there is an infinite cases that need to be checked. No matter how fast your computer is, you can never check infinite cases.
What a computer might possibly do is to randomly come up with theorems. So you start with axioms, and you apply the logical rules on that to come up with new true statements. Given enough time, the compute might (or not) come up with a proof for mathematical statements. But the numbers involved are extremely large here and I don't see this happening any time soon.

5. Nov 7, 2012

Mr.Watson

Well then, will that kind of theorem finding make mathematicians obsolete? Because although you say that not anytime soon, but if somebody would make quantum computer the computing capacity would be unimaginable.

6. Nov 7, 2012

Number Nine

It would be perfectly imaginable; it's being imagined right now in any number of academic journals. It can be quantified precisely. Quantum computers are not miracle devices, they're just very useful.

Part of the problem seems to be that you imagine mathematics to be a collection of calculations or equations, which is not true. Many branches of mathematics don't concern numbers at all, and proofs in these areas involve an extremely long process of logical deduction that often involves techniques from many different fields. It's not as simple as telling a computer (quantum or not) to "Prove the Hodge Conjecture" and then coming back in a week when it's done.

7. Nov 7, 2012

micromass

Unimaginable?? I think you greatly overestimate the power of quantum computing.

8. Nov 7, 2012

Jimmy Snyder

Quantum computing is probabilistic so they are useful for executing probabilistic algorithms. An example is Shor's algorithm for factoring certain composite numbers. I believe the number 15 has been factored this way. Maybe not, but anyway, I changed my public key to 77 just in case. I don't know if such a computer can be used to execute deterministic algorithms.

9. Nov 7, 2012

Staff: Mentor

:rofl:

10. Nov 7, 2012

micromass

According to wiki, they factored 21 already!

11. Nov 7, 2012

AlephZero

12. Nov 7, 2012

Patrick Kale

I was also worried by an idea similar to this, given my knowledge of mathematics and things like that.

13. Nov 7, 2012

Jimmy Snyder

I must be a quantum computer. They left out priest: All the odd numbers are prime.

14. Nov 7, 2012

FreeMitya

I think pop science has distorted people's views on QC.

15. Nov 7, 2012

micromass

Not only on Quantum Computing, sadly enough.

16. Nov 7, 2012

kaos

An interesting perspective on this issue is the notion of NP completeness in computational complexity. Theorem proving is a NP complete problem (a problem that requires an exponential amount of steps to solve((exponential to the size of the inputs )) but can be verified in a polynomial amount of steps).

Quantum computers are not believed to be able to solve NP complete problems efficiently (quantum computers are able to solve BQP complete problems and NP complete is a harder class). The reason is while a QC can represent an exponential number of states in a superposition, it is not clear how to determine which particular state represents the correct answer. There is paper on it by Bernstein and Vazirani (BBBV theorem) but i cant find a source.

There is a good blog for the computer science aspects of QCs here
http://www.scottaaronson.com/blog/?cat=17

But i am not a computer scientist and my view might be mistaken.

17. Nov 7, 2012

No, computers will not replace mathematicians. Computers need humans to tell them what to do.

18. Nov 7, 2012

doubled5

The mind is not made up of fairy dust and unicorns. It is itself a machine. Any and all insights you or anyone have towards math can be replicated by a computer. Super computers of today are not imperceptible relative to the brain in terms of raw computing power; so the jump to quantum computing technologies might not even be a requirement. What you need are good algorithms to simulate thought processes.

19. Nov 8, 2012

symbolipoint

NO! Computers will never make mathematicians obsolete. This is a major point made in the movie, 2001: A Space Odyssey.

20. Nov 8, 2012

Containment

Don't worry about if it'll be useless or not just do what you love. In this current age nobody can really tell you accurately what jobs you might be able to find 5-10 years down the road or what skills it'll take to get the job.

21. Nov 8, 2012

collinsmark

I was about to say that computers will never replace mathematicians, but I'll hold back so as not to risk displeasing our future, robot overlords.

22. Nov 8, 2012

Mr.Watson

Yeah but never mind computers, I mean even some other super-computer could do that kind of theorem solving that micro mass was talking about:

"What a computer might possibly do is to randomly come up with theorems. So you start with axioms, and you apply the logical rules on that to come up with new true statements. Given enough time, the compute might (or not) come up with a proof for mathematical statements. But the numbers involved are extremely large here and I don't see this happening any time soon."

So wouldn't that kind of computers at least replace mathematicians in creating new theorems?

23. Nov 8, 2012

Pythagorean

Computers will make mathematicians who cannot use computers obsolete.

Computers make less demand for researchers to know mathematics... but only because of mathematicians writing computer programs.

24. Nov 8, 2012

micromass

Huh, can you expand?? How does a computer allow a mathematician to know less mathematics?? And how exactly are computers essential in pure math research?

25. Nov 8, 2012

Pythagorean

I didn't say mathematician. I'm talking about science research (including biology). I never learned the Adams mueller bashforth method (or whatever) but I can still solve differential equations using it.

I'm saying mathematicians supply us the benefits from computers so they won't be obsolete.